Implementation within Akantu of smooth contact mechanics with the mortar method

The scope of this project is the implementation of the mortar method for the enforcement of smooth contact constraints in an open-source finite element framework. Smooth contact constraints are rigorously defined, and two approaches to their enforcement (penalty and Lagrange multipliers) are derived rigorously. A detailed description of a complete algorithm for the application of such methods is provided, with a particular attention to the strategies used to tackle non-linearities. Then a brief presentation of the most important features of the implementation of the algorithm is given. To check the correctness of the implementation, several tests are performed: in particular the numerical results are compared with the hertzian solution for a problem of unilateral smooth contact.